Method for determining a coefficient of thermal expansion and apparatus therefor

Abstract

A method for determining the Coefficient of Thermal Expansion of a specimen. The specimen is placed in the tester and a tensile force is applied to the specimen. The specimen is equilibrated at a first temperature and then elongated. After reaching a desired elongation, the specimen is equilibrated at another temperature. The tensile force on the specimen is changed to a predetermined value or until the specimen fails. A force-displacement curve is generated from the stressed specimen. The force-displacement curve is converted into a stress-strain response, from which the Coefficient of Thermal Expansion is determined.

What is claimed is:  
     
       1. A method for determining a coefficient of thermal expansion for a material, comprising: 
       equilibrating the material at a first temperature;  
       imparting a first stress on the material by applying tension to the material;  
       changing the first temperature to a second temperature; equilibrating the material at the second temperature;  
       imparting a second stress on the material by increasing the tension on the material to a second level;  
       determining a stress change of the material; and  
       using the stress change to calculate the coefficient of thermal expansion of the material by graphically determining Young's Modulus using the stress change and a tangential ratio of a stress-strain curve and determining the coefficient of thermal expansion, α, using the equation:        α   =         -   Δ                   σ       E                 Δ                 T                       
       when Young's Modulus and the coefficient of thermal expansion remain substantially constant and where Δσ is the stress change, E is Young's Modulus, and ΔT is a temperature difference between temperatures T1 and T2.  
     
     
       2. A method for determining a coefficient of thermal expansion for a material, comprising: 
       equilibrating the material at a first temperature;  
       imparting a first stress on the material comprising applying tension to the changing the first temperature to a second temperature;  
       equilibrating the material at the second temperature;  
       imparting a second stress on the material comprising increasing the tension on the material to a second level;  
       determining a stress change of the material; and  
       using the stress change to calculate the coefficient of thermal expansion of the material by graphically determining Young's Modulus using the stress change and a tangentia 1  ratio of a stress-strain curve and determining the coefficient of thermal expansion, α, using the equation:        α   =         -   2        Δ                 σ         (     E1   +   E2     )                   Δ                 T                       
       when Young's Modulus is substantially linear and the coefficient of thermal expansion, a, remains substantially constant over the temperature range T1 to T2, where Δσ is the stress change, E 1  and E 2  are Young's Modulus at two points on a stress-strain curve, and T is a temperature difference between temperatures T1 and T2.  
     
     
       3. A method for determining a coefficient of thermal expansion for a material, comprising: 
       equilibrating the material at a first temperature;  
       imparting a first stress on the material comprising applying tension to the material;  
       changing the first temperature to a second temperature;  
       equilibrating the material at the second temperature;  
       imparting a second stress on the material comprising increasing the tension on the material to a second level;  
       determining a stress change of the material; and  
       using the stress change to calculate the coefficient of thermal expansion of the material by graphically determining Young's Modulus using the stress change and a tangential ratio of a stress-strain curve and determining the coefficient of thermal expansion, α, using the equation:            1.5      α2     -     0.5      α1       =         -   Δ                   σ       E                 Δ                 T                       
       when the coefficient of thermal expansion varies linearly with temperature over a temperature range between temperatures T1 and T2 such that α1 and α2 are the coefficients of thermal expansion at temperatures T1 and T2, where Au is the stress change, E is Young's Modulus, and ΔT is a temperature difference between temperatures T1 and T2.